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Build your own Simulator:Understand Free Fall plus a Constant Horizontal Speed
Scenario: My toy airplane is flying 7ft above the ground at a constant horizontal speed of 4 ft/s when its motor falls off. How long before the motor hits the ground? What is the horizontal distance it has traveled?
YouTubeMathcastsorScreenCast Mathcasts (if YT is blocked)
GeoGebra InterActivity Directions for InterActivity READ ME FIRST!
Click on the play button (bottom left) to drop the motor. 1. The green function is height in free fall so for this function the x-axis is time. 2. During that time, the motor is both falling and going forward (at the speed of the airplane) until it hits the ground. The pink curve traces the trajectory of the motor so here thex-axis is distance. When we studied free fall (vertical motion), we only drew the green function. In the future, when we add a horizontal component (projectile motion), we will only draw the pink curve.
DIY: Look at the simulator. Run your mouse over the objects in the Algebra View and the Spreadsheet and/or View -> Construction Protocol. Start GeoGebra and build your own simulator! Complete directions in worksheet.
Good Questions Worksheet (opens in new window)
Sample: Set h0=7 ftand vh=4 ft/sec. Check that v0=0.
The green function h(x) is the vertical motion function for free fall h(x)=h0+v0*x-16x^2.Here the x-axis is time and the y-axis is height of object. The point Ht = (Time, h(Time)) is a point on this function when x=Time. Set Time =0.3 (move the slider or type Time=0.3 in the input bar). Find and explain the meaning of coordinates of Ht? The coordinates of Ht are (0.3,5.56). This says that after 0.3 seconds, the height of the object is 5.56 ft. These coordinates do not show the horizontal distance the object has travelled.
The point Hd = (vhTime, h(Time)). Find and explain the coordinates of Hdwhen Time =0.3. The coordinates of Ht are (1.2,5.56). These coordinates say that the object has traveled horizontally 1.2 ft and is at a height of 5.56 ft. These coordinates do not show the time at which this happens.
Look at the green and pink points (Ht and Hd). Are they the same height? Is it always the case? What is the difference between these two points? Yes, the y-coordinates or the heights are always the same. However, the x-coordinate of Ht is time, whereas the x-coordinate of Hd is horizontal distance. We see that we have 3 variables: time, horizontal distance and vertical height. We cannot graph 3 variables at the same time!However, both the horizontal distance and thevertical heightdepend ontime. So we make what is called a parametric function or curve. This means we keep track of time tand let x=horizontal distance and y=vertical height. This is the pink position curve p(vh*t, h(t)).
Set the initial height of the object h0=7.9 ft. Check that v0=0 ft/sec (since the object is just being dropped). How long does it take to reach the ground? Explain you answer and show the computation. Run the animation. Can you find this result in the algebra view, the graph and the spreadsheet? Is the result the same? "Hitting the ground" means h(t)=0. So 0=7.9-16*t^2 so t=(7.9/16)^0.5=~0.7 sec.
Change the horizontal speed vh to several different values? Does this change the result? Explain. No, because the time it takes for the object to hit the ground depends only on gravity.
.... See the word/pdf documents.
Metadata (includes links for downloads)
Global
Simulation of free fall plus a constant horizontal speed
Brief
InterActivity-Build your own Simulator of a Free Falling Object
play button (bottom left) to drop the motor.
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